Problem: Simplify the following expression: $ x = \dfrac{1}{-4t + 5} + \dfrac{4}{3} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{1}{-4t + 5} \times \dfrac{3}{3} = \dfrac{3}{-12t + 15} $ Multiply the second expression by $\dfrac{-4t + 5}{-4t + 5}$ $ \dfrac{4}{3} \times \dfrac{-4t + 5}{-4t + 5} = \dfrac{-16t + 20}{-12t + 15} $ Therefore $ x = \dfrac{3}{-12t + 15} + \dfrac{-16t + 20}{-12t + 15} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{3 - 16t + 20}{-12t + 15} $ $x = \dfrac{-16t + 23}{-12t + 15}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{16t - 23}{12t - 15}$